document.write( "Question 61323: Help please!\r
\n" ); document.write( "\n" ); document.write( "Solve the system of equations:\r
\n" ); document.write( "\n" ); document.write( "a.2x+y=4
\n" ); document.write( "y=x^2-4x-11\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b. Graph the system of equations:
\n" ); document.write( "y=x^2-2
\n" ); document.write( "y=-2x+1
\n" ); document.write( "label the point(s) of intersection.\r
\n" ); document.write( "\n" ); document.write( "thank you\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #42349 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Solve the system of equations:
\n" ); document.write( "a.
\n" ); document.write( "2x + y = 4
\n" ); document.write( "Rearrange in the general form (y=)
\n" ); document.write( "y = 4 - 2x
\n" ); document.write( ":
\n" ); document.write( "y=x^2-4x-11
\n" ); document.write( "Or
\n" ); document.write( "x^2 - 4x - 11 = y
\n" ); document.write( "Substitute (4-2x) for y, arranage as a quadratic eq, and solve for x:
\n" ); document.write( "x^2 - 4x - 11 = 4 - 2x
\n" ); document.write( "x^2 - 4x + 2x - 11 - 4 = 0
\n" ); document.write( "x^2 - 2x - 15 = 0
\n" ); document.write( "Factors easily to:
\n" ); document.write( "(x-5)(x+3) = 0
\n" ); document.write( "x = +5 and x = -3 are the solutions
\n" ); document.write( ":
\n" ); document.write( "Find the values of y using both solutions:
\n" ); document.write( "x = 5
\n" ); document.write( "y = 4 - 2(5)
\n" ); document.write( "y = 4 -10
\n" ); document.write( "y = -6
\n" ); document.write( ":
\n" ); document.write( "x = -3
\n" ); document.write( "y = 4 - 2(-3)
\n" ); document.write( "y = 4 - (-6)
\n" ); document.write( "y = 4 + 6
\n" ); document.write( "y = +10
\n" ); document.write( ":
\n" ); document.write( "These solutions will be apparent if we graph it:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+6%2C+-20%2C+20%2C+x%5E2+-+4x+-+11%2C+4+-+2x%29+\"
\n" ); document.write( ":
\n" ); document.write( "Notice the points of intersection -3,+10 and +5,-6
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "b. Graph the system of equations:
\n" ); document.write( "y = x^2 - 2
\n" ); document.write( "y =-2x + 1
\n" ); document.write( "label the point(s) of intersection.
\n" ); document.write( ":
\n" ); document.write( "your graph should look like this;
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+10%2C+x%5E2-2%2C-+2x%2B1+%29+\"
\n" ); document.write( ":
\n" ); document.write( "We can calculate the points of intersection by solving for x just like we did in the 1st problem; replace y with one of the equations:
\n" ); document.write( "x^2 - 2 = -2x + 1
\n" ); document.write( "x^2 + 2x - 2 - 1 = 0
\n" ); document.write( "x^2 + 2x - 3 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(x+3)(x-1) = 0
\n" ); document.write( "x = -3 and x = +1 are the solutions
\n" ); document.write( ":
\n" ); document.write( "Find y using both solutions in the 2nd equation, -2x+1:
\n" ); document.write( "y = -2(-3) + 1
\n" ); document.write( "y = +6 + 1
\n" ); document.write( "y = +7
\n" ); document.write( ":
\n" ); document.write( "Using x = +1
\n" ); document.write( "y = -2(1) + 1
\n" ); document.write( "y = -2 + 1
\n" ); document.write( "y = -1
\n" ); document.write( ":
\n" ); document.write( "Our points of intersection: -3,+7 and +1,-1
\n" ); document.write( ":
\n" ); document.write( "Did this make sense to you? Any questions?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );